Differential Shrinkage Prestressed
Differential Shrinkage Prestressed
Differential Shrinkage Prestressed
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S ~ ,,,(1
the differential
+ ,,) + ",(i +
shrinkage
1').. .....
strain
. .(3)
I
in the insitu concrete starts taking place. Hence, the
differential shrinkage between ' the insitu and· precast
concrete is the difference between. the total shrinkage of From the above, the differential shrinkage force is
insitu concrete and the remaining shrinkage in the precast evaluated and hence the stress ar. different fibres can also
beam since the time the composite action becomes effective. be evaluated. . .
Since the insitu concrete is not allowed to shrink. fully
r a force is developed at the interface of the precast and Method 2
i'
~ insitu concrete. This force acts as a tensile force on the
In this method, a pair of tensfrle iorces is applied at the
insitu concrete and as a compressive force on the precast
II
. two ends of the ir.situ slab till the elastic deformation of
beam.
the slab equals the differential shrinkage. The two concretes
The actual quantum of shrinkage depends on the are then clamped and an equal and opposite force is
various factors; viz. the cement in the mix, the water- applied to the composite sectipn at the centre of gravity
cement ratio, grade of concrete, surface area of. the of the in~itu slab. '1 J:~
diff9rential shrinkage force is
exposed surface. percentage of reinforcement, age of evaluated III the following manner
concrete, humidity, etc. The author does not intend to
~
,,; . evaluate the actual shrinkage of the precast and insitu
F = AiES
concretes in this article: r nly the effect of differential
The stresses at different fibrels can be evaluated following
shrinkage on the str~cLUre will-be investigated,
thevarious steps stated in thisl method. . . '
The examples given in the .Appendix show how the
.
India'L,imited, Maker Tower 'E'; Cuf{o
. the modulus of elasticity of r
. stresses obtained by, these two , methods vary.
__ .. It can be seen that where the section properties and
the insitu and precast
I
!
FEBRUARY 1984 47
i
l~c- "'"
-~"-·"··-······"r·-·'·'_>'"""".,, ••
~.•~ ..•..•
~ ~~+-.,
/'
'..-
-1
'~
N01ATIONS
Ac = area of composite section S = differential shrinkage between the precast
= A" + Ai.f:i..· . beam and the insitutlab
Ep 8;m . = slope of insitu slab lue to the action of
= A~+ Ai T differential shrinkag+. force at interface
Ai = Area of insitu concrete slab. B,sw = slope of insitu slab due to self weight of
AT = transformed area of insitu concrete
insitu slab I
Ap r area of the precast concrete beam 8pM = slope of precast beam due to action of
ei = distance of the centre of gravity of the differential shrinkag~force at interface
insitu concrete slab from the interface
!
e" = distance of the centre of gravity of the
Yib = distance of the cent~e of gravity of the
insitu section from Hottom
precast beam from the interface
Yit = distance of the cent¥ of gravity of the
z. = modulus of elasticity of insitu concrete slab
insitu section from top
t: = modulus of elasticity of the precast
Y'b = distance of the centre of gravity of the
concrete beam
= strain due to differential shrinkage force' p;ecast section froml bottom
Eii
of insitu concrete slab at the level.of interface Ypt = distance of the centie of gravity of the
= strain due to differential shrinkage force precast section from top
Ep;
of precast beam at the level of interface
z.: = section modulus of composite section at
.f,J, = stress at top of insitu slab
z;
bottom of precast concrete
= section modulus of domposite section at
fit = stress at top of insitu slab
j;'h = stress at bottom of precast beam the junction of insitJ and precast concrete
/,.1 = stress at top of precast beam ZCI = section modulus' of composite section at
F = force due to differential shrin'cage z;
top of insitu concrete
J; = moment of inertia of the insitu slab = section modulus of ihsitu slab at the
II' = moment of inertia of the precast concrete bottom of insitu slab
beam Zit '= section modulus of insitu sieib at the top
Mi = Fe, of i~situ slab 1 .
sections are same then the stresses are also same, Table Method 3: The eccentric forc~s dlle to differentialshrinkage . 'OJ
. 3, But when the section properties of the precast beam at the interface cause a moment along the entire length of
are far more than those of the insitu slab then not only the precast beam and insitu slab, due to w::ich both the
do the stresses vary by a wide margin but also the stresses precast beam and the insitu s~ab will deflect. The quantum
at the top fibres of the insitu concrete are opposite in .of deflection/rotation will depend on the values of
. . I .
nature, i.e. compressive in method 1 and tensile in
M d M. . I rotation.
which cause such de flcctron ..
r"" .
j
'method 2, Table 1. It is also noted that the differential - an -I!.
. shrinkage force in ei ther case is several times higher-in- E;li ,_. E/p , ._.
case: of method 2 than in case of method 1. Case 1, when the slope of precast element is smaller
than that of insitu element - Fig 1 shows the differential
Anomaly in compatibility in methods 1 and 2 shrinkage force acting at the interface. Due to such force
In both these two methods compatibility is not fully the precast beam which is supported at the two ends will
satisfied as is shown below. . --deflect downwards. and thel insitu slab will deflect like
a cantilever, FiR 2. If theseparation of the insitu slab
Method J: The differential shrinkage -lorce has been is permitted then there will not be any force acting at
assumed to act at the interface and with this force acting . the interface over the lengf' of separation. Hence, this
as an eccentric force, the stresses are calculated. Fig 1. problem has been dealt wit in the following two steps.
Fig 2 shows how the deformations will take place when
the force, F acts eccentrically. . - (i) step 1 - the insitu sl~b i allowed to be lifted off but
the differential s nnkage force acts in horizonal
If. the values
. 0
f ..
M, - and
M"
,.... - f insitu
0 I
'.' an d precas t direction alOng~1 e entire length of the compo-
E/,. E"I" I site beam as if t e shear connectors which are
fixed to the prcast beam are put in rigid
units respectively are different then the slopes of insitu and
precast elements will also be different and since the insitu frictionless hollqw sleeves which are in turn
and precast units are connected together and no separation fixed to the insiu slabalong the entire length
is permitted, the compatibility is disturbed. This pheno- of the composit1 beam, Fig 3.
menon has been considered in this paper in method 3. I r- I nsitu
II' . \
(b)
l'~
u.~~~~n~g
Insilu
lh
1I
i
7;'
F-----[-...-.-~::,os t
Net difference 'in slope between
the precast beam, Fig2
=(B;M-Bis..)-BpM
=8r
the insitu slab and
, (c)'
PL3 , PL3
The slope at the end G{ the insitu slab due 10 the self 8, =.= .,- -. - 't..- .. (II)
weight of the slab .' ... AL,,1p 24£/;
WL2 L 1
.8jsw = - x-x - ..(6) From equation (11) the falces in the vertical ties 'per
8 6 E;l; unit length can be calculatedr .
Now if(OiM. - O;.J '" iI.,mthen there will not be any The examples worked OUI!using method 1 and 2 ha~e
..also been worked out with method 3.. The stresses in
uplift of the insitu "jab ana hence no separation. linueh-'
a case the insitu slab will follow the curvature of the precast various fibres have been cOlPared in Tables 1 to 3 for
these 3 methods.
beam and the moment on the insitu slab will be modified
to .. It can be seen that the st esses obtained by method
, 0 3 are similar to those o~taired by method 2 both in
M = j rei X ...!'H_
°rM "" r .
I
-Insi t.u
ln~ilU'
Pr.CQsl
.. -Sh.o r
t...JW-.::I.:::Z::::r===="==="'===L . con n C tor s IZ
.
. ~
. .
__. Pre:cast t-s he Q reo n n 12 e ue r s
f
~ ~ ! l ------J.-----t.
I
\
i/.
Fig 3 Shear connectors along the entire
beam
length of composite
Fig'4 TO, deflected form of r"'"" and insitu "em en's
l FEBRUARY.1984 49
!i
I
I
".
,I
I
'Appendi" ~
3,35 m
1
v Precast girder
o
\----Prqctlst b ec m lnsitu slab
'"
<0,
N
A, = 6700cm' t, = 22. 3333cm'
~ Zit = Zib = 22333. 3ems
Yi, = Yib ='lOcm I E; = 2.82x lO'kg/cm'
lY 1'1-"""
~
self weight of insitu slab
Stressesaccording
-6
to method 1
r F
J lS.08kg/cm
\
Fx 10 ]
/
Cement and C'HlLrCIC Association.' November 1%3. II 536B 14tll6 \ 16Jl670 X 3."'52
k
3: BANERJEE,S. P. Differential shrinkage effects in composite structures.
International Association for Bridge and Structural Engineering, 10.26kgfcm' (tension)
publication vol. 31-II. 1971, pp. 15-29.
4: VENKATESULU, G, and BAPU. SATYANARAYANA.'Practical -,fih 188940 _
[ 5368
188940 _
14816
18:8940 :; 81.62 '12:82
\ 2048934 3,52
:-
approach to the problem of differentialshrinkage stresses in composite
construction of prestressed and insitu concrete used in bridge decks.
Indian Highways. August 1974,pp. 22-27. 14.92kg/cm· (tension)
,-;
'"
: [pt -
. 188~0
[ 14816 "
188940 x 81.62
.J..
2048934
J Insiui slab
Ai
Zit
= 22Scm)
= = 281.2Scm I
lib J
1 t,
Yit
1055cm'
Yib =3.7Scm
'\
Example 2
Since 8isw > 8im the insitu S[bb will deflect lollowing the slope of
This comp~site beam has a span of 3m. The differential shrinkage is the precast beam. !' ,
100 X 10- .
Therefore, the modified mo en! of the insitu slab will be
Precast beam
'Ap = 225cm' Ip = 1055cm' M:=Fx 3.75 X
132.84
i65.8
Zpt = Zpb =
281.2Scml Ypt = Ypb = 3.75cm I
FEBRUARY 1984 51
I
! .;7'
').;~
"
&;;;;?"
~f -~~•..
-::~.-~
.•.•
- -~-~,-- ..,.....-
..--'~-:-r-- .. -'~ ••""-'-""-'- ,,~~-,.,r,- .....
-.. ._.". ~,,__ . - __
___ .-: .•.._-.I:_.• _·._·~_~~ .f._._-....·.•.~ .._ ~~. - ---~~~~~ --.......•..~
1\ ~
""y
Now writing the equilibrium equation with the revised moment TABLE 2 Differenti:11 stres~,?,,,
I
,·.Jr example
.
2
JOO
.
y. 10
-6
=
[F225 +
. 3F]
281.25 "Q')
1
v 1m
+ At stress, kg/em'
point
method J method 2 method 3
F F x 3.75
[ 225 + 281.25 ] '1 "'1 1~_ 1(.•6 -7.8 -6.66 -6
(compression) (compression) (compression)
Solving F = 952kg. 2 15.6 (tension) 14'r (rensien) 14.38 (tension)
3 -15.6 -17V . -J6.85
• ( 1 .~) (compression) (compression) (compf.:5sion)
: [it = 952 225 - 28}.25 4 7.8 (tension) 13.22 (tension) 8.47 (tension)
./
1 3.75 )
[pI = - 952 ( + 225 + 281.25 TABL:E3 Differentiallstresses for example 3
.!
):
A large number of projects of various kinds are under execution all over the country, most of t~em using concrete in one
way or another. Many of these projects have interesting features. Many present technical problfms which require all the
ingenuity of the constructional engineer to resolve. Readers of this Journal are keenly interested' in reading about
all this and we shall therefore, particularly welcome worthwhile contributions bearing on- ~o~truc~; ';', They' should be
accompanied by good black and white glossy photographs.
I ~I.
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